Byron York has an interesting post on a new Granite State poll of possible 2016 presidential primary contenders in New Hampshire. While York focuses on the bad news for Mark Rubio (he is now at 2%), the most striking feature of the poll is actually the lack of headway Rand Paul is making among GOP voters, despite the good press that Paul has been getting and the fact that many pundits seem to believe he is the presumptive GOP nominee.

Rand Paul is currently leading the race with 15% among likely primary voters, just edging out Kelly Ayotte (13%) and Chris Christie (12%). The Granite State poll does not define “likely primary” voter. However, a good guess would be that a likely voter is a registered Republican who has voted in a previous GOP primary.

Now, Ron Paul received 23% of the vote in the 2012 New Hampshire primary. However, as it is an open primary, he received only 14% of the vote of registered Republicans. According to exit poll data, much of Ron Paul’s support in New Hampshire in 2012 came from people who ended up voting for Obama in the general election, or who sat out the general election.

Given that Ron Paul received only 14% of the vote of registered Republicans in New Hampshire in 2012, at present Rand Paul is doing no better than his father in New Hampshire. Recall that because of its open primary, New Hampshire was the high water mark of the Ron Paul campaign in 2012. The vast majority of other states had closed primaries, making 14% the ceiling of support Ron Paul would receive among GOP voters.

Of course, if the vote were held today, it is impossible to know what Rand Paul’s final tally would be in New Hampshire, because we cannot really gauge the amount of Democratic crossover vote he would get, and because 15% of respondents in the Granite State poll said that they were still undecided.

The 2016 primaries are still a long way away, and no one can predict all of the twists and turns that will occur between now and then. However, this poll gives evidence that Rand Paul has not been able to make much of an inroad with people in the GOP who refused to support his father. And, if he has not been able to do this thus far, given the tailwind he has had at his back for the last two years, it is unlikely that he will do better with GOP voters by primary day.